Ummm... your datasheet clearly says 8V typical Forward Voltage drop, max fwd current per segment of 60mA etc. You shd probably stay closer to 30mA per leg. You should be able power it through a 9V battery with current limiting resistors.
The key thing to note is you'll need to use arduino to "switch" segments on & off since Arduino Uno digital pins can't give u more than 5V - the simplest way (and the messiest) would be to use transistor switches for each segment http://en.wikipedia.org/wiki/Transistor#Transistor_as_a_switch
. I'm sure if you want to get more sophisticated u can Google on MOSFETs etc :-)
PS: Just noted 1 more complexity - your decimal point
- marked DP in the datasheet takes only 4V
and not 8V. I think the device would have been better designed if it took only 1 supply voltage - but if you don't need it, simply don't connect the decimal point to your circuit :-)